CONRAD Code Research Articles

Estimation of Covariances on Prompt Fission Neutron Spectra and Impact of the PFNS Model on the Vessel Fluence

As the need for precise handling of nuclear data covariances grows ever stronger, no information about covariances of prompt fission neutron spectra (PFNS) are available in the evaluated library JEFF-3.2, although present in ENDF/B-VII.1 and JENDL-4.0 libraries for the main fissile isotopes. The aim of this work is to provide an estimation of covariance matrices related to PFNS, in the frame of some commonly used models for the evaluated files, such as the Maxwellian spectrum, the Watt spectrum, or the Madland-Nix spectrum. The evaluation of PFNS through these models involves an adjustment of model parameters to available experimental data, and the calculation of the spectrum variance-covariance matrix arising from experimental uncertainties. We present the results for thermal neutron induced fission of 235 U. The systematic experimental uncertainties are propagated via the marginalization technique available in the CONRAD code. They are of great influence on the final covariance matrix, and therefore, on the spectrum uncertainty band width. In addition to this covariance estimation work, we have also investigated the importance on a reactor calculation of the fission spectrum model choice. A study of the vessel fluence depending on the PFNS model is presented. This is done through the propagation of neutrons emitted from a fission source in a simplified PWR using the TRIPOLI-4 ® code. This last study includes thermal fission spectra from the FIFRELIN Monte-Carlo code dedicated to the simulation of prompt particles emission during fission.

A Covariance Generation Methodology for Fission Product Yields

Recent safety and economical concerns for modern nuclear reactor applications have fed an outstanding interest in basic nuclear data evaluation improvement and completion. It has been immediately clear that the accuracy of our predictive simulation models was strongly affected by our knowledge on input data. Therefore strong efforts have been made to improve nuclear data and to generate complete and reliable uncertainty information able to yield proper uncertainty propagation on integral reactor parameters. Since in modern nuclear data banks (such as JEFF-3.1.1 and ENDF/BVII.1) no correlations for fission yields are given, in the present work we propose a covariance generation methodology for fission product yields. The main goal is to reproduce the existing European library and to add covariance information to allow proper uncertainty propagation in depletion and decay heat calculations. To do so, we adopted the Generalized Least Square Method (GLSM) implemented in CONRAD (COde for Nuclear Reaction Analysis and Data assimilation), developed at CEA-Cadarache. Theoretical values employed in the Bayesian parameter adjustment are delivered thanks to a convolution of different models, representing several quantities in fission yield calculations: the Brosa fission modes for pre-neutron mass distribution, a simplified Gaussian model for prompt neutron emission probability, theWahl systematics for charge distribution and the Madland-England model for the isomeric ratio. Some results will be presented for the thermal fission of U-235, Pu-239 and Pu-241.

Generation of238U Covariance Matrices by Using the Integral Data Assimilation Technique of the CONRAD Code

A new IAEA Coordinated Research Project (CRP) aims to test, validate and improve the IRDF library. Among the isotopes of interest, the modelisation of the 238 U capture and fission cross sections represents a challenging task. A new description of the 238 U neutrons induced reactions in the fast energy range is within progress in the frame of an IAEA evaluation consortium. The Nuclear Data group of Cadarache participates in this effort utilizing the 238 U spectral indices measurements and Post Irradiated Experiments (PIE) carried out in the fast reactors MASURCA (CEA Cadarache) and PHENIX (CEA Marcoule). Such a collection of experimental results provides reliable integral information on the (n,γ) and (n,f) cross sections. This paper presents the Integral Data Assimilation (IDA) technique of the CONRAD code used to propagate the uncertainties of the integral data on the 238 U cross sections of interest for dosimetry applications.

Feedback on 239Pu and 240Pu nuclear data and associated covariances through the CERES integral experiments

Benchmark measurements of irradiated and un-irradiated fuel samples were performed in the framework of the CERES collaborative program between AEA (UK Atomic Energy Agency) and CEA (French Atomic Energy Commission). These experiments provide relevant data for the validation of fuel burn-up and criticality-safety calculations for the whole fuel cycle. As part of this program, pile-oscillation measurements were carried out on a range of mixed-oxide samples with plutonium of various mass and isotopic contents, both in the MINERVE and DIMPLE reactors. Four core configurations, two over-thermalized situations and two pressurized water reactor (PWR)-type situations, were constituted with different forward and adjoint flux spectra, emphasizing fission and/or capture contributions. The experiments were analyzed using reference TRIPOLI4 calculations with the JEFF-3.1.1 library, using exact three-dimensional models of the core configurations. In a first step, calculations of each DIMPLE configuration were performed and compared with the experiment, showing very good agreements with a maximum C-E of −230 pcm. In the second step, reactivity worth experiments were analyzed, using recently developed exact-perturbation capabilities in TRIPOLI4. A consistent assimilation of calculation over experiment discrepancies was performed with the CONRAD code, using the integral data assimilation method. Covariance matrix on multigroup neutron cross sections and multiplicities were generated and significant trends were identified, especially on the 239Pu and 240Pu capture cross sections in the thermal energy range (E < 0.1 eV). Further investigations should be required to confirm these conclusions, due to the strong dependence of these trends and of posterior covariances to prior covariances.

Covariance Matrix Evaluations for Independent Mass Fission Yields

Recent needs for more accurate fission product yields include covariance information to allow improved uncertainty estimations of the parameters used by design codes. The aim of this work is to investigate the possibility to generate more reliable and complete uncertainty information on independent mass fission yields. Mass yields covariances are estimated through a convolution between the multi-Gaussian empirical model based on Brosa's fission modes, which describe the pre-neutron mass yields, and the average prompt neutron multiplicity curve. The covariance generation task has been approached using the Bayesian generalized least squared method through the CONRAD code. Preliminary results on mass yields variance-covariance matrix will be presented and discussed from physical grounds in the case of 235U(nth, f) and 239Pu(nth, f) reactions.

Study on Prompt Fission Neutron Spectra and Associated Covariances for 235U(nth,f) and 239Pu(nth,f)

Prompt Fission Neutron Spectra (PFNS) are very important nuclear data for reactor neutronic calculation tools. Most of the international evaluated nuclear data libraries lie on the Madland-Nix model, which is a based on evaporation theory of fission fragments. But very scarce data can be found regarding the PFNS covariance matrix associated to these evaluations. As an illustration of the impact of the PFNS on neutronic calculations, we will show a Monte-Carlo calculation of the neutron flux received by a PWR vessel, using different PFNS evaluations. The neutrons that have the highest probability to contribute to the vessel flux are those that are emitted at the highest energies; however most of the fission neutrons are emitted around 2 MeV. These results show the necessity to have very precise PFNS evaluations, and a proper estimation of associated covariances. The estimation of the PFNS covariance matrix associated to a model, after adjustment of model parameters, will be shown. This is performed by the CONRAD code, developed at CEA Cadarache. The final goal of the study is to adjust the parameters involved in fission fragments de-excitation in the FIFRELIN Monte-Carlo code, also developed at CEA Cadarache, which computes the PFNS among other fission quantities, and to provide the associated PFNS covariance matrix. However for the moment we focused the study on three historically widely used PFNS models: Maxwellian, Watt and Madland-Nix models. The covariance matrix on the adjusted spectrum comes mainly from the systematic uncertainty on some experimental parameters — namely the normalization, background, detection efficiency, etc. In order to propagate this type of uncertainties properly, the marginalization technique is used. A close knowledge of the conditions in which a particular experimental PFNS has been measured is required, in order to have a correct estimation of the PFNS uncertainties after adjustment. In this work, we propagated the uncertainty on normalization of experimental spectra, and the uncertainty on the energy-dependent neutron detection efficiency. We show the resulting PFNS and associated covariance matrix in the case of thermal neutron-induced fission of 235U and 239Pu.

Recent Developments in the CONRAD Code regarding Experimental Corrections

The CONRAD code is an object-oriented software tool developed at CEA Cadarache since 2005 to deal with problems arising during the evaluation process (data assimilation and analysis, physical modelling, propagation of uncertainties…). This paper will present recent developments concerning the experimental corrections, which are required when a neutron resonance shape analysis is performed. Several experimental aspects are detailed in this work:

Validation of capture yield calculations in the Resolved Resonance Energy Range with CONRAD code

This paper deals with the validation of the multiple scattering corrections developed in the CONRAD code for the capture yield calculations in the Resolved Reso- nance energy Range (RRR). In order to calculate the capture yields, analytic and stochas- tic calculation schemes implemented in CONRAD are described and compared with the analysis code SAMMY/SAMSMC. The results are in excellent agreement for a variety of samples. We concentrate the discussion here on 238 U, 197 Au and 55 Mn.

Covariances for 239Pu Induced Cross Section in the Resonance Range using the CONRAD Code

Covariances for 239Pu Induced Cross Section in the Resonance Range using the CONRAD Code

Statistical Analysis of a Set of Actinide Resolved Resonance Parameters with CONRAD Code

Statistical Analysis of a Set of Actinide Resolved Resonance Parameters with CONRAD Code

Uncertainty evaluation of nuclear reaction model parameters using integral and microscopic measurements. Covariances evaluation with CONRAD code

In the [eV;MeV] energy range, modelling of the neutron induced reactions are based on nuclear reaction models having parameters. Estimation of co-variances on cross sections or on nuclear reaction model parameters is a recurrent puzzle in nuclear data evaluation. Major breakthroughs were asked by nuclear reactor physicists to assess proper uncertainties to be used in applications. In this paper, mathematical methods developped in the CONRAD code[2] will be presented to explain the treatment of all type of uncertainties, including experimental ones (statistical and systematic) and propagate them to nuclear reaction model parameters or cross sections. Marginalization procedure will thus be exposed using analytical or Monte-Carlo solutions. Furthermore, one major drawback found by reactor physicist is the fact that integral or analytical experiments (reactor mock-up or simple integral experiment, e.g. ICSBEP, …) were not taken into account sufficiently soon in the evaluation process to remove discrepancies. In this paper, we will describe a mathematical framework to take into account properly this kind of information.

Average neutron parameters for hafnium

The neutron transmission of natural hafnium samples have been measured within the 2 eV to 50 keV energy range at the white neutron source GELINA of the Institute for Reference Materials and Measurements (IRMM) in Geel, Belgium. Data sets for two temperatures (77 K and 300 K) and three sample thicknesses (1 mm, 2 mm, 15 mm) have been simultaneously analyzed in terms of Reich–Moore parameters. The ESTIMA technique in association with the generalized SPRT method were used to obtain a consistent set of l-dependent average resonance parameters. For each hafnium isotope, scattering radius R ′ , neutron strength function S l , distant level parameter R l ∞ , mean level spacing D l and average radiation width 〈 Γ γ 〉 are given and compared with results reported in the literature. The capture and total cross sections calculated by the CONRAD code using this set of average parameters were successfully compared to experimental data retrieved from EXFOR.